Dynamic Programming: Knapsack - Equal Partition (Partition Equal Subset Sum)
What is the space complexity of the top-down memoization solution for Equal Partition with n elements and total sum S?
What is the space complexity of the top-down memoization solution for Equal Partition with n elements and total sum S?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze memoization storage
Memo stores results for states (i, curr_sum), total O(n * S) entries.Step 2: Consider recursion stack
Recursion stack depth is O(n), memo size O(n*S), but stack is separate.Final Answer:
Option A -> Option AQuick Check:
Space = memo + recursion stack = O(n*S) + O(n) ≈ O(n*S) [OK]
Quick Trick: Memo + recursion stack space combined [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming only memo space counts
Trap Explanation:
PITFALL- Candidates often forget recursion stack adds to space complexity.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space in recursive DP
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